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AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES
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 Title & Authors
AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES
Park Jong-Jin; Zhang Yong;
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 Abstract
We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on , then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.
 Keywords
average shadowing property;-average-pseudo-orbit;shadowing property(pseudo orbit tracing property);-pseudo-orbit;chain recurrent;
 Language
English
 Cited by
1.
SOME PROPERTIES OF THE STRONG CHAIN RECURRENT SET,;;;

대한수학회논문집, 2010. vol.25. 1, pp.97-104 crossref(new window)
1.
Asymptotic average shadowing property on compact metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 2008, 69, 9, 2857  crossref(new windwow)
2.
Parameterized IFS with the Asymptotic Average Shadowing Property, Qualitative Theory of Dynamical Systems, 2016, 15, 2, 367  crossref(new windwow)
3.
On partial shadowing of complete pseudo-orbits, Journal of Mathematical Analysis and Applications, 2014, 411, 1, 454  crossref(new windwow)
4.
h–Average-Shadowing Property and Chaos, Journal of Dynamical Systems and Geometric Theories, 2013, 11, 1-2, 39  crossref(new windwow)
5.
On partial shadowing of complete pseudo-orbits, Journal of Mathematical Analysis and Applications, 2013, 404, 1, 47  crossref(new windwow)
6.
Diffeomorphisms with C 1-stably average shadowing, Acta Mathematica Sinica, English Series, 2013, 29, 1, 85  crossref(new windwow)
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